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Keywords:

  • life-cycle;
  • modelling;
  • population growth;
  • shooting;
  • survival rate

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

1. Bird populations can be efficiently managed only if the demographic mechanisms that cause change are correctly understood. Here we illustrate the demographic variables causing decline among grey partridge Perdix perdix populations in France by comparing populations that show contrasting trends. The analysis combined a field survey at 10 contrasting sites during 3 years, modelling and statistical analyses; survival rates and reproductive success were estimated through the largest-ever radio-tracking study of hens, while density was estimated through counts.

2. Population viability analyses showed that, in France, north-western populations of grey partridge were healthy whereas south-eastern populations were declining.

3. Elasticity analyses accounting for environmental stochasticity indicated that the survival rate during shooting, over winter and at the time of the first nesting attempt were the most important demographic influences on population growth rate. The hatching rate, covey size at hatching of first clutches and chick survival rate were secondary. The contribution of replacement clutches to population change was low.

4. Multiple regression showed that hen survival during the first nesting attempt explained 33% of the variability in the population growth rate across populations. The shooting pressure increased with the health of the population.

5. Improving survival rate during winter and the first nesting attempt was not sufficient for recovery in a declining population. It was also necessary to increase simultaneously the hatching rate of first clutches and chick survival rate to produce a stable population that could sustain shooting.

6. Low hen survival rates, in particular during the breeding period, explain the recent decline of grey partridge populations in some regions of France. However, the recovery of populations will need a simultaneous improvement of several demographic parameters.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Many birds species are currently believed to be threatened with global extinction, and many non-threatened species are reported to be in decline (Hagemeijer & Blair 1997). Among them are several species of Galliformes (Rands 1992) such as the grey partridge Perdix perdix L., a widespread game bird of open farmland (Carroll 1993). During this century, populations have declined seriously in many regions (Tucker & Heath 1994), as suggested by the reduction of shooting bags (Birkan & Jacob 1988; Potts & Aebischer 1995). Because the grey partridge is an economically important game bird, the decline of this species has become an important management concern. As a result, the grey partridge is listed among species with unfavourable conservation status in Europe (Hagemeijer & Blair 1997).

Effective management to recover populations depends upon correctly diagnosing limiting demographic variables. Thus, many authors have examined the demographic traits that most affect population fluctuations (Blank, Southwood & Cross 1967; Podoler & Rogers 1975; Manly 1977; Potts 1980; Potts & Aebischer 1991, 1995). Chick survival has large effects on population fluctuations, but overwinter survival rate (Manly 1977) and nest predation (Potts & Aebischer 1991, 1995) might also be important.

In north-central France, stable densities of wild grey partridge could have been maintained at a medium or high level (Reitz 1992) through the limitation of shooting bags (Reitz 1996, 1997). Yet a decline in adult annual survival rate continued after this measure (Reitz 1997; Reitz & Mayot 2000). This demographic trend has raised concerns about the conservation of this species and the future of harvesting (Reitz 1996), so that better diagnosis of demographic effects is now crucial. One possibility is that decline could be attributable to a decrease in hen survival rate during breeding (Reitz 1990; Reitz & Berger 1993). To investigate this hypothesis, we conducted a large field survey by radio-tracking breeding hens in contrasting farming regions. Simultaneously, we recorded the environmental characteristics of the study sites. The global objective of this study was first to compare the demographic patterns of declining and stable populations of grey partridge, and second to correlate demographic differences with environmental factors (Green 1995). This paper reports the first step of this analysis using a combined approach of modelling and statistical analyses. First, we built a life-cycle model (Caswell 1989) detailing reproductive events in order to make the model relevant to both partridge breeding biology and current ecological problems faced by the grey partridge. The model was used to (i) estimate population growth rates through population viability analyses (Boyce 1992), and (ii) to assess the elasticity of the population growth rate to changes in demographic variables in a fluctuating environment (Tuljapurkar 1990). Secondly, we investigated which demographic variables explained the variations in the population growth rate across study sites by using multiple regression. We examined whether changing crucial demographic variables of a declining population could restore a stable and harvestable population.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Study areas

Ten study sites located in north-central France (Fig. 1) were monitored during 1995–97. The study areas displayed a wide range of farmland landscapes (Bro 1998). Land use was traditional farming (mixed arable and livestock) in areas A, B, C, D and H, whereas other areas were located in open farmlands supporting intensive cereal production. The main crops were cereals (range of availability on the total arable area across study sites: 30–60%), maize (0–25%), beet (0–20%), potato (0–18%), sunflower (0–8%), oilseed rape (0–7%) and forage crops (3–28%). The availability of crops and the abundance of permanent cover such as pastures (0–12%), linear habitats (1·4–9·1 km ha−1), and groves (0–17%) varied across study areas. Mean field size ranged from 1·5 to 10 ha. Weather conditions were those of a mild temperate climate. The topography was flat to gently undulating.

image

Figure 1. Map. of north-central France showing the location of the 10 study sites monitored in 1995–97. Study site A: Flandres (2000 ha); B: Artois (2006 ha); C: Picardie (7633 ha); D: Pays de caux (1500 ha); E (6000 ha), F (5300 ha) and G (7000 ha): Champagne crayeuse; H: Val-de-Loir (6000 ha); I: Beauce (15200 ha); and J: Gâtinais (5320 ha). The name of three administrative departments are given as a future reference. Hatching refers to Paris and its suburbs. Thin and thick lines are the limits of two levels of administrative divisions.

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Field procedures

The demography of the grey partridge was monitored on each study site through radio-tracking of hens during spring and summer, and by counts in early spring and late autumn. Radio-tracking was chosen because it allowed estimates of survival rate of radio-tagged hens, location of nests and surveys of chicks (White & Garrott 1990). We captured 1009 hens in early spring (mid-late March) and radio-tagged them with a small necklace radio-transmitter weighing about 10 g (Bro, Clobert & Reitz 1999). Hens were monitored daily until mid-September. Clutches could be located when incubation had started because hens only left their clutches once or twice a day during incubation (Potts 1980; Birkan & Jacob 1988). Clutches were mostly visited after hens had left (i.e. after hatching, desertion or destruction) in order to minimize predation and desertion risks. A total of 407 first clutches and 141 replacement clutches was described (clutch size, fate, number of hatched eggs). Clutch fate was determined according to clutch state: hatching was recognized by small regular breaks in the egg shell (Birkan & Jacob 1988); clutch desertion was deduced when intact but cold eggs were found (hen alive); and clutch destruction was indicated by broken eggs. We surveyed the broods of 101 radio-tagged hens, and counted the number of surviving offspring at 6 weeks after hatching.

Counts were conducted in mid-March and early December on the 10 study sites to estimate the density before reproduction and after the shooting season, respectively. We counted the number of partridges flushed while fields were beaten by a line of people (Birkan & Jacob 1988). Age of birds could not be determined during counts.

Data analysis

Throughout, the dynamics of the 10 populations of grey partridge were considered as independent (this is a fundamental requirement in comparative analysis; Green 1995) because study sites were too far away from each other (cf. Fig. 1) for fluxes among them to be likely (Potts 1980; Birkan & Jacob 1988).

Age effects on demographic performances were tested by comparing, at an individual scale, the difference of demographic estimates between hens in their first breeding season and older hens, controlling for year and site effects. In the case of a continuous dependent variable, age effects were analysed through either a multiple anova (proc glm; SAS Institute 1994) or a non-parametric analysis (proc npar1way; SAS Institute 1994) when assumptions of linear models were violated. Age effects were tested through a logistic model (proc genmod; SAS Institute 1994) when the dependent variable was a binary or a proportion variable (binomial distribution, logit link function, controlling for overdispersion) or a count variable (Poisson distribution, log link function, controlling for overdispersion). Density-dependence was tested at the population scale (i.e. by using a mean estimate of variables per site and year) through a regression analysis (proc reg; SAS Institute 1994) where both the dependent (a demographic variable) and the independent (the density) variables were log-transformed (log10). We tested whether the spatio-temporal variability (taken as a measure of the environmental stochasticity) of demographic variables could be adjusted to Gaussian distributions by using the Wilk–Sharpino test (proc univariate; SAS Institute 1994). Correlation analyses between pairs of continuous variables were performed by using Pearson coefficients (proc corr; SAS Institute 1994). To identify the demographic variable(s) that best explained the differences in the population growth rate, we performed a backward multiple regression analysis (proc reg; SAS Institute 1994). We tested whether demographic variables differed between two groups by using a t-test controlling for heteroscedasticity (proc ttest; SAS Institute 1994).

Modelling

The demographic model

Model structure. We built a female life-cycle model. Usually, these models assume an instantaneous reproductive event (the so-called ‘birth-pulse’) and a survival rate of breeders of one during breeding (Caswell 1989; Noon & Sauer 1992). Because these assumptions were irrelevant for the grey partridge, which display a seasonal peak of mortality during the breeding season (Bro 1998), we explicitly modelled reproductive events and survival of breeders to investigate the effects of breeding hen mortality on the reproductive success and population dynamics.

In the model, census occurs in early spring, before breeding (Fig. 2). We assume that all the females pair and lay a clutch, because the spring sex ratio was reported to be male-biased (Birkan & Jacob 1988) or at least balanced (Potts 1980). Clutches fail when the hens die during laying or incubation (hen survival rate: S1). Environmental factors may also lead to clutch failure (hatching rate of first clutches: α). The number of offspring issuing from first clutches is computed as the product of covey size at hatching (Hatched1) and offspring survival rate (Sj1), assuming a balanced primary sex ratio. Hens whose first clutches fail may renest (renesting rate: β). Those that do not renest survive until the shooting period with the same survival rate as hens with offspring (survival rate: S2). Replacement nesting is modelled in the same way as the first nesting (hen survival rate during laying and incubation: S3; hatching rate of replacement clutches: γ; hen survival rate after clutch hatching or failure: S4; offspring survival rate: Sj2). The population is harvested, so the mortality in autumn is attributable to shooting (survival rate: S5). The hens present in late autumn that survive over winter (S6) breed the next spring.

image

Figure 2. Life. -cycle model of the female grey partridge. The model details the reproductive events, in particular hen survival during breeding. In spring, all females attempt to breed. Clutches fail either when hens that are laying or incubating die or when adverse environmental conditions destroy eggs. When first clutches fail, surviving hens may lay replacement clutches. Replacement clutches may hatch or not, as for first clutches. Breeding hens in the next spring are those that survive shooting and over winter. S1: hen survival rate during laying and incubation of first clutches; α: hatching rate of first clutches; Hatched1: number of hatched eggs in successful first clutches; Sj1: survival rate of chicks issuing from first clutches to the age of 6 weeks; β: renesting rate of hens the first clutch of which failed; S2: survival rate of hens after their first clutch hatched or failed with no renesting; S3: hen survival rate during laying and incubation of replacement clutches; γ: hatching rate of replacement clutches; Hatched2: number of hatched eggs in successful replacement clutches; Sj2: survival rate of chicks issuing from replacement clutches to the age of 6 weeks; S4: hen survival rate after replacement clutch hatched or failed; S5: survival rate during the shooting season; S6: overwinter survival rate.

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This model structure is a mere demographic description of population dynamics, based on the species' life cycle, and not on relationships with particular environmental factors such as in Potts's model (Potts 1980; Potts & Aebischer 1991). Nevertheless, environmental conditions appear through demographic estimates and their variations.

Age effects. Contrasting results have been reported for age effects on grey partridge survival and clutch size. Some authors reported no difference in overwinter survival rate between adults and fledglings (Potts 1980), whereas others found that offspring had a lower overwinter survival rate than adults (Birkan & Jacob 1988; Church & Porter 1990). Similarly, some authors reported no difference in clutch size with regard to age (Potts 1980; Birkan & Jacob 1988) whereas others found that 1-year-old hens had a higher fecundity than older hens (Blank & Ash 1960). We modelled only one age class because we did not find any age effect on survival rates and reproductive success (Table 1).

Table 1.  Age effects on demographic variables tested at an individual scale through a multiple regression (F-tests) or logistic regression (χ2 tests), controlling for site and year effects. Saw: survival rate during autumn and winter; it was estimated with hens radio-tagged in September-October and monitored until mid-March (for more details see Bro, Clobert & Reitz 1999 ). Sss: hen survival rate during spring and summer; it was estimated from mid-late March to mid-September by using the Kaplan–Meier method with radio-tagged hens monitored > 7 days. Hatched1: number of chicks at hatching for first clutches, α: hatching rate of first clutches, Sj: survival rate of chicks to the age of 6 weeks
Demographic variableStatisticP
SawF1,10= 0·080·781
SssF1,44 = 0·250·621
Hatched1χ12 = 0·120·728
αχ12 = 0·620·432
Sjχ12 = 0·500·478

Density-dependence. Density-dependence is an important demographic phenomenon that has been reported for recruitment (Rands 1987), brood production rate (Potts 1980; Panek 1997), nest losses (Aebischer 1991) and overwinter survival rate (Aebischer 1991; Rotella et al. 1996; Tapper, Potts & Brockless 1996). However, some analyses used to detect density-dependence are likely to raise some statistical concerns (Lebreton & Clobert 1991). Because we did not detect density-dependence in hen survival rate during spring and summer (survival increased with breeding density), overwinter survival rate, hatching rate, covey size at hatching and chick survival rate (Table 2), we did not model density-dependence on these parameters. However, density-dependence occurred through shooting pressure (see below).

Table 2.  Density-dependence on demographic variables tested at a population scale through a multiple regression, controlling for site and year effects. All variables but S6 (calculated as the spring to autumn density ratio) were estimated independently from density. Density-dependence of Sss, Hatched1, α and Sj was tested against spring density, of S6 against autumn density. Abbreviations as in Fig. 2 and Table 1
Demographic variableStatisticPPartial r2Intercept (mean ± SE)Slope (mean ± SE)n
S6F1,15 = 0·840·3740·05−0·09 ± 0·31−0·08 ± 0·0917
SssF1,26 = 4·800·0380·16−1·21 ± 0·220·19 ± 0·0928
Hatched1F1,26 = 1·480·2340·052·73 ± 0·21−0·10 ± 0·0828
αF1,26 = 0·440·5110·02−1·04 ± 0·300·08 ± 0·1228
SjF1,23 = 1·440·2420·06−1·88 ± 0·640·31 ± 0·2625

Shooting. We modelled the shooting pressure (i.e. the number of birds shot during the shooting season km−2) as a density-dependent kill of a surplus (Aebischer 1991). In a given year, the shooting pressure limits aim to ensure, from the current density in early autumn (Da), a target breeding pair density for the next spring (Ds), assuming a predicted overwinter survival Sw (set to 0·6; Reitz & Berger 1995). Thus, survival rate during the shooting season (S5) is given by:

  • image(eqn 1)

This formula assumes that the winter mortality is additive to the mortality occurring during the shooting season.

Stochasticity. A deterministic model regards all individuals of the population as identical to an ‘average individual’, and demographic parameters are constant through time. Both of these assumptions are not realistic, so we incorporated into the model demographic and environmental stochasticity (Lebreton & Clobert 1991; Benton & Grant 1996; Legendre 1996). Demographic stochasticity refers to the chance that an individual has to survive and to breed. We modelled demographic stochasticity by using a binomial distribution for survival, and a Poisson distribution for the number of chicks produced by a successful clutch (for further details about modelling see Legendre & Clobert 1995; Legendre 1996). The Poisson distribution is commonly used because it is the distribution of counted positive data (McCullagh & Nelder 1989). Environmental stochasticity refers to environmental perturbations that affect survival and reproduction similarly for all individuals of a same class. Environmental stochasticity was modelled by using a Gaussian distribution (Legendre & Clobert 1995; Legendre 1996). The Gaussian distribution is commonly used because it is symmetrical and bell shaped around the mean, and it matched our field data (Table 3). The Poisson and Gaussian distributions were both truncated in order to be relevant with regard to biological values: survival rates varied between 0·01 and 0·99, covey size at hatching between 8 and 16 chicks for first clutches and between 6 and 14 chicks for replacement clutches (these values were the maximum and minimum values we actually observed).

Table 3.  Adjustment tests of spatio-temporal variability of demographic variables to Gaussian distributions. The Wilk–Sharpino test of normality is commonly considered as significant when P < 0·01. Abbreviations of demographic variables as in Fig. 2 and Tables 1 and 2
Demographic variableDescription of the distribution of the demographic variable
Test of normalityMeanSD
WP
S60·8920·0290·6760·175
Sss0·9770·7710·4960·138
Hatched10·8970·00812·32·4
α0·9590·3390·4580·157
Sj0·9490·2050·4050·229
Estimation of model parameters

Most model parameters were estimated through data recorded by radio-tracking breeding hens. Indeed, the monitoring of our radio-tagged hens, of their clutches and their broods, provided detailed data such as the proportion of surviving hens at each stage of the life cycle during breeding, the proportion of successful clutches, the number of chicks produced by successful clutches and the proportion of surviving offspring at 6 weeks after hatching. Thus it was possible to estimate directly (i.e. as proportions or means) almost all model parameters. Separate estimates were calculated for each study site and year.

  • 1
    . The survival rate during the first nesting attempt (S1) was estimated as the proportion of radio-tagged hens surviving from capture and release until their first clutch hatched or failed. We did not take into account censoring that occurred within the first week after release because we had evidence of adverse effects of radio-transmitters on survival (Bro, Clobert & Reitz 1999).
  • 2
    . The hatching rate of first (α) and replacement clutches (γ) was estimated as the proportion of successful clutches (i.e. for which at least one egg hatched).
  • 3
    . The covey size at hatching of first (Hatched1) and replacement clutches (Hatched2) was estimated as the mean number of eggs that hatched in successful clutches.
  • 4
    . The renesting rate (β) was estimated as the proportion of hens whose first clutch failed and that laid a replacement clutch.
  • 5
    . The offspring survival rate (Sj) was estimated as the proportion of chicks that survived to the age of 6 weeks. This parameter was first estimated for each covey we monitored through radio-tagged hens. Then, in the second step, we computed the mean value over all coveys monitored per study site and year. In the model, we separated Sj for chicks issuing from first (Sj1) and replacement clutches (Sj2) but we set the same value for both parameters because we had too few data to estimate Sj1 and Sj2 separately.
  • 6
    . The hen survival rate after nesting was estimated as the proportion of hens that survived from hatching or failure of their first clutch until mid-September (S2), and from hatching or failure of their replacement clutch until mid-September (S4).
  • 7
    . The hen survival rate during laying and incubation of replacement clutches (S3) was estimated as the percentage of hens surviving from the failure of their first clutch until their replacement clutch hatched or failed.

We used counts to estimate overwinter survival rate (S6). This apparent survival rate (i.e. including immigration and emigration fluxes) was computed as the early December count to mid-March count ratio. This estimate was the realized value of the hypothesized value Sw used to calculate shooting pressure limits (see equation 1).

We did not estimate a separate temporal variability for each study site otherwise it would have relied only on a 3-year temporal series per site. We assumed that the environmental stochasticity of a given variable was measured by the standard deviation of estimates across study sites and years (i.e. spatio-temporal variability). Consequently, we also assumed that the environmental stochasticity was the same for all study sites. The data did not allow separation of temporal and sampling variances as proposed by Link & Nichols (1994); sampling variance was assumed to be small compared with the spatio-temporal variance.

A summary of main demographic characteristics of all study sites is given in Table 4.

Table 4.  Main demographic characteristics of grey partridge populations monitored in 1995–97 on the 10 study sites in north-central France. Spring breeding pair density (Ds, no. pairs km−2, mean area counted in ha) and autumn density (Da, no. birds km−2, mean area counted in ha) were estimated through counts in March and early December, respectively. Hen survival rate during breeding (Sss) was estimated through radio-tagged hens monitored > 7 days by using the Kaplan–Meier method (survival rate from mid-late March until mid-September; total number of hens monitored). The reproductive success was estimated through a covey survey in August (no. offspring aged > 6 weeks per hen; total number of coveys observed). The shooting pressure is the number of birds shot in autumn per km2. The overwinter survival rate (S6) was estimated as the spring to autumn density ratio. Standard deviations (SD) correspond to across-year variability of the mean, no SD means that data were available for only 1 year. The symbol ‘/’ indicates that data were not available
Demographic variableStudy site
ABCDEFGHIJ
Breeding density27·9 ± 0·619·5 ± 3·210·8 ± 2·727·5 ± 5·47·1 ± 1·46·4 ± 1·19·2 ± 1·62·9 ± 1·111·3 ± 1·614·9 ± 4·8
(2800 ha)(1110 ha)(1400 ha)(1220 ha)(2090 ha)(1920 ha)(2480 ha)(1930 ha)(5390 ha)(1720 ha)
Autumn density/43·3 ± 13·328·4 ± 1·770·4 ± 11·823·2 ± 3·318·8 ± 2·133·4 ± 96·8 ± 0·436·6 ± 5·845
(359 ha)(1133 ha)(877 ha)(1634 ha)(1726 ha)(2497 ha)(1550 ha)(4442 ha)(2287 ha)
Hen survival rate during breeding 0·60 ± 0·13  0·47 ± 0·12 0·65 ± 0·06 0·60 ± 0·11 0·42 ± 0·04 0·27 ± 0·04 0·43 ± 0·08 0·51 ± 0·12 0·44 ± 0·08 0·58 ± 0·15
(89)(104)(75)(87)(83)(88)(96)(31)(94)(101)
Reproductive success5·0 ± 1·55·7 ± 0·46·2 ± 0·46·5 ± 1·66·6 ± 1·25·4 ± 1·75·8 ± 0·87·9 ± 2·96·8 ± 1·26·4 ± 1·8
(146)(100)(107)(148)(96)(79)(209)(16)(366)(185)
Shooting pressure27·1 ± 0·318·6 ± 1·78·0 ± 1·114·5 ± 12·6 0·2 ± 0·4 0·60 ± 0·55 0·3 ± 0·3/3·5 ± 0·75·6
(3394 ha)(1423 ha)(2728 ha)(1667 ha)(5600 ha)(4500 ha)(7000 ha) (10020 ha)(7270 ha)
Overwinter survival rate/ 0·92 ± 0·11 0·83 ± 0·08 0·72 ± 0·03 0·48 ± 0·01 0·65 ± 0·18 0·56 ± 0·05 0·90 ± 0·150·70 ± 0·03 0·49 ± 0·01
Simulation of population dynamics – population viability analysis

Population dynamics were simulated according to:

  • image(eqn 2)

where N(t) is the number of breeding hens in early spring at time t, and λ is the population growth rate. Time units (t) are years. The population growth rate is a function of the maternity function m and the annual survival rate S:

  • image(eqn 3)

The growth rate of a population in a deterministic scheme corresponds to the first eigenvalue (λ1) of the transition matrix (Caswell 1989). A analogue of λ1 may be defined under a stochastic scheme by an estimator (Tuljapurkar 1990; Metz, Nisbet & Geritz. 1992; Benton & Grant 1996), called hereafter λstocha. This stochastic population growth rate was calculated from Monte Carlo simulations according to (Legendre 1996):

  • image(eqn 4)

where T is the number of time steps, M the number of trajectories, and Nj(t) the population size of the trajectory j at time t. This formula takes into account the extinct trajectories (i.e. when Nj(t) = 0 then ln(Nj(t)) = 0), so it includes in some way the extinction probability. The accuracy of the estimation was ensured by a high number of trajectories (Benton & Grant 1996) from which we estimated the variance of λstocha by using the usual formula:

  • image(eqn 5)

The extinction of a population is a chance event that results from demographic stochasticity and temporal random variations of life-history variables. The probability of extinction was computed as the proportion of extinct trajectories (Legendre 1996).

Population dynamics were run for 10 years (so T = 10), and 1000 replicates were completed for every Monte Carlo simulation (so M = 1000) to ensure statistically reliable predictions. A new random generator seed was selected for each simulation, and values of demographic parameters varied randomly at each time step (Legendre & Clobert 1995; Legendre 1996). Initial population size for a given study site corresponded to the number of breeding hens on a 10-km2 area. This number was calculated from the breeding pair density (mean estimate across 1995, 1996 and 1997; Table 4).

We used the unified life model (ULM) software (Legendre & Clobert 1995; Ferrière et al. 1996; Legendre 1996) to run the model.

Stochastic elasticity analysis

The sensitivity assesses the effects of small variations in a model parameter x on the population growth rate (Caswell 1989). However, when parameters are measured on different scales, the direct comparison of their sensitivity may be difficult or misleading. To allow comparisons, we used elasticities, the elasticity e being a proportional change in the population growth rate for a given variation in a parameter x (Caswell 1989). High elasticity is an indicator that a small change in a parameter has large effects on the growth rate of the population. Recently, some authors have claimed that environmental fluctuations should be taken into account to assess the true effect of a change in a demographic parameter on the population growth rate (Tuljapurkar 1990; Van Tienderen 1995; Benton & Grant 1996; Steen & Erikstad 1996; Erhlén & Van Groenendael 1998). To this end, these authors proposed several different methods. The method computed in the ULM software was the generalized analogue of Caswell's formula developed by Tuljapurkar (1990):

  • image(eqn 6)

where T is the number of time steps, A(t) the transition matrix at time t, aij a matrix element, V(t) the left eigenvector (i.e. the reproductive value) and W(t) the right eigenvector (i.e. population structure) at time t (Tuljapurkar 1990; Legendre 1996). The symbols ‘•’ and ‘〈〉’ denote scalar products. This formula assumes demographic ergodicity and the absence of temporal autocorrelation. We performed elasticity analyses taking into account the environmental variability of parameters (hereafter stochastic elasticity coefficients) running one trajectory for 250 time steps, without demographic stochasticity.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Spatial variation of the population growth rate

Populations of grey partridge displayed large differences in their growth rates. In a constant environment, study sites could be divided into two groups according to demographic status: the populations were growing at study sites A, B, C, D and I, whereas they were declining at study sites E, F, G, H and J (Table 5). The most healthy populations were A and D in the north-west of France, and the least healthy populations were E, F and G in Champagne (Fig. 1). In a fluctuating environment and under demographic stochasticity, the stochastic growth rates (mean (λstocha), hereafter λstocha to simplify) were lower than in a constant environment (all were below one) but we found similar results in the sense that populations A and D had the highest λstocha (higher than 0·95) whereas populations E, F, G and J had a λstocha as low as 0·65. Populations B, C, I and H had an intermediate λstocha (Table 5). Except for site I, a geographical north-west/south-east contrast in the grey partridge population health appeared. Low λstocha was associated with a high extinction rate of trajectories, and extinction occurred over a short term (Table 5). We emphasize that these values have to be taken as projections and not predictions (Caswell 1989); moreover, they have to be considered as relative values in a comparative approach (i.e. across study sites) and not as absolute values.

Table 5.  Population growth rates in a deterministic environment (eigenvalue, λ1) and viability analysis (model with both demographic and environmental stochasticity, and shooting) of the 10 populations of grey partridge under study. Mean (λstocha) is the mean stochastic growth rate estimated over 1000 trajectories (equation 4, standard errors of λstocha were negligible, i.e. < 0·01). P(ext) is the probability of extinction over 10 years, T(ext) is the mean time of extinction (standard errors were < 0·1)
Deterministic environmentStochastic environment
Study siteλ1Mean (λstocha)P(ext)T(ext)
A1·5860·9820/
B1·1200·8570·0608·0
C1·0880·8590·0588·5
D1·4540·9610·0038·0
E0·3770·6530·9984·4
F0·5090·6620·9695·3
G0·6430·6450·8856·3
H0·7730·7330·8176·3
I1·1940·8500·1128·1
J0·6370·6210·8086·8

Model validation

We verified the model based estimates of λstocha in two ways. First, we investigated the relationship between λstocha and breeding density; this latter variable was taken as a mirror of both carrying capacity and population dynamics. Estimates of λstocha were positively correlated with the breeding pair density (r10 = 0·759, P = 0·011; Fig. 3). This correlation is a piece of evidence that, in a comparative approach, the differences in estimates of λstocha computed through modelling matched differences in some aspects of field observation. Secondly, we compared our results to independent data provided by the national routine population survey of grey partridge (the time trend of breeding density and estimates of annual survival rate) in three administrative departments (‘Somme’, ‘Seine maritime’ and ‘Aube’; Fig. 1). These data partly validated model-based estimates of λstocha. Indeed, we could rank the Aube and Somme departments in the same order as λstocha did: breeding density and annual survival rate were higher in the Somme than in the Aube (see the Appendix). The survival rate of the grey partridge has declined recently through out France (Reitz 1997), but we could observe two contrasting situations: the survival rate remained higher than 0·4 in some regions such as in the Somme, whereas it felt down to low values (0·25) in other regions such as in the Aube (Appendix).

image

Figure 3. Positive. correlation between the growth rate (mean (λstocha)) of the 10 populations of grey partridge and their breeding density in spring (mean ± SD across years). Capital letters identify study sites (cf. Fig. 1).

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Contribution analysis

The contribution analysis was performed in two steps. First, the elasticity analysis in a variable environment assessed the relative effects of changes in demographic parameters on λstocha. One separate analysis was performed for each study site. We observed three groups of variables according to their stochastic elasticity coefficients (Fig. 4). The most important parameters were the survival rate during the shooting season (S5), the overwinter survival rate (S6) and the hen survival rate during the first nesting attempt (S1), followed by the hatching rate of first clutches (α), the covey size at hatching (Hatched1) and the survival rate of chicks issuing from first clutches (Sj1). The effect of hen survival after hatching (S2) on λstocha was small. The success of first clutches was more important for λstocha than successful replacement clutches (Fig. 4). This hierarchical group order was the same for all study sites but with some cosmetic differences in the rank order of parameter importance within each group. However, the difference in the stochastic elasticity between the first and second ranked parameters was negatively correlated with λstocha (r10 = −0·636, P = 0·048). This meant that the relative importance of hen survival rate from early autumn until the end of the first nesting attempt for λstocha, compared with the reproductive success, increased when the health of the population decreased.

image

Figure 4. Stochastic. elasticity coefficients of model parameters; mean ± SD across study sites. Hen survival rate from the shooting season until the end of the first nesting attempt (S5*S6*S1) was the most important parameter for the population growth rate mean (λstocha). The success of first clutches was more important for mean (λstocha) than the success of replacement clutches. Abbreviations of demographic variables as given in Fig. 2.

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Secondly, we aimed to identify the demographic variables (among the ones previously pinpointed as important in the elasticity analysis, in order to reduce the number of variables in the analysis) that were responsible for differences in λstocha. A first multiple regression analysis showed that the shooting pressure was positively linked to λstocha (F1,13 = 45·3, P < 0·001, r2 = 77·7%; Fig. 5a). This result confirmed that the shooting pressure was dependent on the demographic health of the population, as recommended by the current shooting management regime. When removing this variable from the analysis, only variations in hen survival rate during the first nesting attempt (S1) explained 33% of the variation in λstocha (Table 6 and Fig. 5b).

image

Figure 5. Relationships. between (a) the shooting pressure in the 10 populations of grey partridge and their population growth rate (mean (λstocha)) and (b) the population growth rate (mean (λstocha)) and the hen survival rate during the first nesting attempt (S1); mean ± SD across years.

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Table 6.  Backward multiple regression analysis between mean (λstocha) and the demographic variables pinpointed as the most important by the stochastic elasticity analysis (i.e. hen survival rate over winter and during nesting, success of first clutches). Abbreviations as in Fig. 2
Demographic variableStatisticPPartial r2
S3F1,10 = 0·180·679< 0·01
Hatched1F1,11 = 0·250·6260·01
αF1,12 = 2·560·1360·07
S6F1,13 = 2·280·1550·14
Sj1F1,23 = 1·270·2710·13
S1F1,28 = 13·630·0010·33

Effects of demographic changes in a declining population on population status

We wanted to compare the demographic patterns of declining and stable populations. For this purpose, we created two ‘fictional’ populations by gathering some ‘real’ populations that were similar regarding both their geographical location in north-central France and their λstocha. We chose on the one hand populations E, F and G, and on the other hand populations A and D. Hence, we defined two hypothetical populations: ‘Champagne’ (average of E, F and G) and ‘Nord’ (average of A and D). The demographic patterns of these populations were contrasting for only three demographic variables: overwinter survival rate (S6, T5·5(unequal variances) = −3·12, P = 0·023) and hen survival rate during the first nesting attempt (S1, T13(equal variances) = −5·05, P < 0·001) were higher in the Nord than in the Champagne population, whereas we observed the opposite pattern for covey size at hatching of first clutches (Hatched1, T13(equal variances) = 5·02, P < 0·001) (Fig. 6). The other variables did not differ significantly (P > 0·05), in particular hatching rate of first clutches (α, T13(equal variances) = −1·67, P = 0·119) and chick survival rate (Sj, T13(equal variances) = −1·48, P = 0·164). These differences led to a contrasting population status: the Nord population was stable whereas the Champagne population was declining with a high probability of extinction in the short term (Table 7a). Increasing the values of either S6 or S1 in the Champagne population upwards to the values observed in the Nord population (Table 7b) improved its demographic status (increase in λstocha, decrease in the extinction risk) but not enough to produce a stable population (Table 7b). Increasing the values of both variables S1 and S6 upwards to the values observed in the Nord population led to a more stable population. However, if the management objective for this game species is to recover a population that sustains shooting, it appeared necessary to improve two other demographic variables, namely hatching rate of first clutches and chick survival rate (Table 7b), although they did not differ significantly between the Nord and Champagne populations.

image

Figure 6. Comparison. between the demographic patterns of the hypothetical Champagne (average of sites E, F and G; black circles) and Nord (average of sites A and D; white circles) populations. All variables are scaled on the left axis, except Hatched1/2 scaled on the right axis; mean ± SE across real populations. Abbreviations of demographic variables as given in Fig. 2. The symbol ‘*’ denotes significant differences (t-test, P < 0·05).

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Table 7.  (a) Population viability analysis of the two hypothetical Nord and Champagne populations. (b) Effects of changes in demographic variables on mean (λstocha) for the hypothetical Champagne population by setting S1, S6, α and Sj to the values observed in the hypothetical Nord population. Abbreviations of demographic variables as in Fig. 2, of population viability analysis as in Table 5
(a) Hypothetical populationMean (λstocha)P(ext)T(ext)
Nord0·9790/
Champagne0·6510·9615·75

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Following the method proposed by Green (1995), we conducted an intraspecific comparative analysis of contrasting populations to pinpoint the demographic variables that were likely to drive the decline of grey partridge in France. We found that some populations are stable whereas other are declining, but estimates of population growth rate (λstocha) must not be taken as absolute and predictive values of λstocha; these are just projections that have to be examined in a comparative approach. The λstocha is the most elastic to variations in the hen survival rate from the shooting season to the end of the first nesting attempt, and also to the success of first clutches and chick survival rate. Replacement clutches are of lower importance, as previously suggested by Reitz (1992). The hen survival rate during the first nesting attempt is the only factor significantly explaining the variations in λstocha across the 10 populations we studied.

The combined approach of monitoring and modelling, which was previously claimed to be a useful tool for managers (Potts & Aebischer 1991), introduced some points of discussion in our work. First, demographic variables were mostly estimated through radio-tracking. We previously gave evidence of adverse effects of radio-transmitters on grey partridge (Bro, Clobert & Reitz 1999), therefore we corrected survival rates for these effects by taking into account only hens monitored for longer than 7 days. We could not exclude effects on the reproductive success but they were less marked than for survival (Bro, Clobert & Reitz 1999). Secondly, the estimation of environmental variability was based on a 3-year time series on 10 contrasting sites. Methodological studies have warned against bias due to the mean (McArdle, Gaston & Lawton 1990), the sampling variance (Link & Nichols 1994) and the length of the time series (Cyr 1997) in estimates of temporal variability. Unfortunately, our data did not allow us to correct for these biases. However, the model was run with the same amount of environmental stochasticity in the simulation of all populations, thus contrasts in λstocha across populations are unlikely to result from differences in uncorrected bias in environmental stochasticity estimates. Thirdly, using a modelling approach necessarily implies a model structure and underlying assumptions. Our model structure tried to capture the population dynamics of the species by reproducing as faithfully as possible its life cycle, in particular during the reproductive period (first and replacement nesting events were modelled). We tested or justified all the main assumptions of the model (age effects, density-dependence, shooting pressure) or used the most parsimonious assumptions (primary sex ratio). These three weaknesses are likely to be of lower importance in a comparative approach. Indeed one may assume that biases are similar in all sites. Moreover, model outputs were partly validated by independent data provided by the national routine survey of grey partridge populations, and by convergent results from other analyses (Bro 1998).

The identification of key demographic variables is important in understanding population dynamics and guiding management actions. Earlier studies have outlined the key importance of chick survival rate in population dynamics of grey partridge (Blank, Southwood & Cross 1967; Podoler & Rogers 1975; Potts 1980). Field studies provided experimental validation of this result. Indeed, reduction in insect abundance has been shown to be related to intensive use of pesticides (Southwood & Cross 1969) by modern farming (Potts 1997) and was shown to be the main cause of the decrease in chick survival rate (Green 1984; Rands 1985, 1986; Sotherton & Robertson 1990; Borg & Toft 2000). This is a plausible and convincing scenario that is likely to explain the decline of the grey partridge. However, no trend in chick survival rate has explained the more recent decline in grey partridge density (Green & Hirons 1991), suggesting that other variable(s) may play a role in the decline. Our results support this hypothesis: hen survival rate during the first breeding attempt rather than chick survival rate explains the variations in λstocha across our 10 study sites, and the data from the national routine survey of partridge populations provide evidence of a statistically significant decline in survival rate in recent years (Appendix). Similar results have also been found in England: Potts & Aebischer (1995) showed that the brood production rate (i.e. a combination of adult and clutch survival rates) has been declining since the 1970s.

After identifying key parameters, the next step for a manager is to investigate whether increasing these parameters could halt the decline and recover the population. We found that increasing a single demographic variable in a declining population upwards to its value observed in a stable population would not allow a stable population. A stable population sustaining density-dependent harvesting could only be produced by improving four parameters simultaneously: overwinter survival rate, hen survival rate during breeding, hatching rate of first clutches and chick survival rate. These results differ from those of Potts & Aebischer (1995), who showed that an increase in offspring survival rate alone could stabilize most of the declining populations.

Management implications

The ecology of the grey partridge has been studied extensively and this knowledge provides three guidelines for management actions to try to halt population decline thought to be due to current threats: adjustment of shooting pressure, predator control and habitat management. In France, shooting has been strongly limited or prevented altogether in areas where grey partridge density has fallen to low values (Reitz 1996; Appendix). This decision was based on the perceived need for local conservation of grey partridge, but it was not sufficient to halt the decline in survival rate of grey partridge. Therefore, other management actions must be taken to act simultaneously on several demographic parameters, for instance increasing both the survival rate over winter and during breeding, and improving the reproductive success through a reduction in clutch destruction rate and chick mortality rate. These improvements could be achieved, at least in part, through seasonal control of some predator species that are responsible for losses (Birkan & Jacob 1988; Tapper, Potts & Brockless 1996), through habitat management such as the supply of quiet winter and nesting cover, and by enhancing chick food through the protection of field margins (Potts 1997; Borg & Toft 2000).

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

We thank M. Massot and E. Danchin who reviewed an earlier draft of this paper and kindly provided constructive criticisms. Two anonymous referees provided valuable comments that helped very much in the revision of the manuscript. We gratefully acknowledge the editors Dr Ormerod and Dr Kerby for all their editorial comments that gave clarity to our paper and improved our faulty English. We extend our thanks to a large number of individuals who participated in the design and execution of this study. The field study was funded and supported by the Office National de la Chasse and the Union Nationale des Fédérations Départementales de Chasseurs. The Fédérations Départementales de Chasseurs of Aube, Loiret, Marne, Nord, Pas-de-Calais, Sarthe, Seine maritime and Somme provided the technical support for the field survey. We gratefully acknowledge all the field technicians who collected the data; P. Mayot helped F. Reitz to co-ordinate the field survey. We thank the landowners and the hunters for their co-operation in the study.

References

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  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix
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Appendix

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix
Time trends of breeding density and annual survival rate since 1990

We verified whether model-based estimations of the population growth rate (mean (λstocha)) were congruent with (i) the time trend of breeding density and (ii) the time trend of annual survival rate estimates. These data were provided by the independent data set of the national routine population survey (breeding density, reproductive success and shooting pressure). Data were recorded each year on many large areas located in north-central France. The breeding density and the reproductive success were estimated from counts in March and censuses in August, respectively. We estimated annual survival rates as described by Reitz (1992).We measured the trend in breeding density and in annual survival rate from the time series provided by the national routine survey as the slope of the log–linear regression of density/survival rate (dependent variable) against year (independent variable) (Greenwood et al. 1995). We tested whether the slope was statistically negative, null or positive (proc glm; SAS Institute 1994). To take into account spatial variability, we treated counted areas as a random variable.

Analyses were performed for only three administrative departments that contained a study site (Somme, Seine maritime, and Aube; Fig. 1) because no or insufficient data were available for the other departments.

  • 1
    . In the Aube department, we could not detect a significant decline in the mean breeding density since 1990 (which ranged between 4 and 10 pairs km−2; F1,55 = 1·82, P = 0·202). We observed an increase in density in the early 1990s followed by a decrease in 1995 despite a drastic reduction in shooting pressure (Fig. 7). Study sites F and G reflected correctly both the density and the shooting situations of the Aube in 1995–97 (Fig. 7). Low densities could be explained by a low annual survival rate (Fig. 8); contrary to breeding density, we detected a significant decline in annual survival rate (F1,50 = 16·33, P < 0·001, slope =−0·107 ± 0·027 SE). Annual survival rate was around 0·4 in the early 1990s but dropped to 0·25 in 1994–95.
  • 2
    . In the Seine maritime department, the mean breeding density did not decline (F1,185 = 0·84, P = 0·359; Fig. 7); it has varied between 10 and 25 pairs km−2 since 1990. The study site D did not reflect the situation of the department, at least in 1995–97: it was a high density area compared with the mean density in the ‘Seine maritime (Fig. 7). Unfortunately, time series were insufficient to detect a trend in annual survival rate over the last 10 years (Fig. 8).
  • 3
    . The breeding density in the Somme department has not declined since 1990 (F1,105 = 1·24, P = 0·278; Fig. 7). Mean densities were higher than 20 pairs km−2; in comparison, the study site C was a low density area in 1995–97 (Fig. 7). The annual survival rate declined slightly from 0·5 in 1990–91 to 0·43 in 1997–98 (F1,100 = 3·52, P = 0·063, marginal probability, slope =−0·025 ± 0·013 SE; Fig. 8).
image

Figure 7. Time. trends of breeding density (circles) and shooting pressure (triangles) on three administrative departments, Aube, Seine maritime and Somme (Fig. 1), since 1990; mean ± SE, number of areas where counts were performed. The situation of study areas F–G, D and C in 1995–97 are also given (same scale to allow comparison).

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image

Figure 8. Time. trend of annual survival rate estimates in three administrative departments, Aube, Seine maritime and Somme (Fig. 1), since 1990; mean ± SE, number of areas where counts were performed.

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The data provided by the national routine survey of grey partridge populations validated model outputs imperfectly because (i) the time series were not of equal quality across the Aube, Seine maritime and Somme departments, and (ii) study sites did not reflect the situation of their corresponding department. However, we could rank the Aube and Somme in the same order as that given by the mean (λstocha): spring density and annual survival rate were higher in the Somme than in the Aube (Figs 7 and 8). The survival rate of the grey partridge has declined recently throughout France (Reitz 1997), but we could observe two contrasting situations: the survival rate remained higher than 0·4 in some regions such as in the Somme, whereas it declined to low values (0·25) in other regions such as in the Aube (Fig. 8).